Phrases Previous Year Questions (PYQs) – Ratio And Proportion

Investment Doubling Problem

A man invests Rs. 5,000 in each of the years 1990, 1995, 2000, and 2005.
His investment doubles every 5 years.
Find the total amount he receives in 2010.

Doubling period = 5 years

For each investment, amount in 2010 is calculated as:
$$A=P\times 2^{\frac{t}{5}}$$ where
$P=$ principal (Rs. 5,000),
$t=$ years invested (difference between 2010 and investment year).

• Investment in 1990 (20 years):
  $$A=5000\times 2^{\frac{20}{5}}=5000\times 2^4=5000\times 16=80000$$
• Investment in 1995 (15 years):
  $$A=5000\times 2^{\frac{15}{5}}=5000\times 2^3=5000\times 8=40000$$
• Investment in 2000 (10 years):
  $$A=5000\times 2^{\frac{10}{5}}=5000\times 2^2=5000\times 4=20000$$
• Investment in 2005 (5 years):
  $$A=5000\times 2^{\frac{5}{5}}=5000\times 2^1=5000\times 2=10000$$

Total Amount in 2010 = $80000+40000+20000+10000=\boxed{{\displaystyle 150000}}$ Rs.